Math can be a tough subject especially when you start adding more numbers! Two digit addition can be a struggle for students. This can become even more difficult when you add all the changes that we have made to the math curriculum over the years. However, there are newer ways to teach “New Math” that will make two digit addition a breeze. All you need to do is combine regrouping and new math!
Why Use New Math?
New math was created because studies show that people who were good at math learned using these techniques. While parents often teach kids regrouping at home, it’s important we use what we know works. Which one works? Both work together well if you use these simple methods.
Melding New Math and Regrouping
Instead of choosing which one is best, I like to teach new math and regrouping together. Why? Some students get math when they learn the regrouping method, and it’s something that parents often teach them at home. However, some kids just don’t get regrouping, so doing other methods, like partial sums, might meet their learning needs.. Therefore, I like to hit them with several different techniques to figure out what way works best for that student. This “noodle theory” (throwing things against the wall and seeing what sticks) is what got me to use partial sums.
Combine Regrouping and New Math
For this example, we are going to say we are adding 45 plus 23.
Teaching with Partial Sums Using the V Method
The first thing you’re going to do is write 45+23 across the top of the white board or paper. Students are going to add the two ends together and then the ones together. Because we have written it horizontally, we are going to make two “Vs” to show what we are adding together.
It’s important during this step that you remind students they are really adding 40 and 20 because of the place value of the numbers. To reinforce this idea, write 40 + 20. Then, under the other V you world write 5+3.
To simplify this, I’m going to put the 5+3 under the 40+20 as well. Now, 40+20 is simply for students to do if they understand that it’s 4-10’s plus 2- 20’s because 4+2 is six, all you need to do is add the “tens” or the 0. Now, I move the 5+3 under the 40+20=60.
Now I’m going to add 5+3 together to get 8. Then I finish the math problem 60+8 is 68. In other words, 6 10s plus 8 equals 68.
Combine Regrouping and New Math with the Open Number Line
To combine regrouping and new math with an open number line, we are going to use the same equation and make sure to add the 10s together again. However, this time we are going to it with a stronger visual by using an open number line. An open number line is a number line that doesn’t have anything on it to start.
For this method of combining regrouping and new math, you’re not going to start with zero or one on your number line. Instead, you’re going to start with 45 because that is the first number in the equation. Then, you’re going to look at 23. The number is 2 tens and 3 ones.
Because I know this is 2 tens, I’m going to make two jumps of 10 by drawing them on my number line and labeling them with the number ten.
Now that I have made my two big jumps of 10, my 45 has turned to 65. Make sure you show students it is 65 because 45+10 is 55 and 55+10 is 65.
Finally, you just have to add your three little ones that are left. That’s how I get the answer: 68. This is the same answer I got before, so it must be the correct answer.
These two techniques that combine regrouping and new math take a lot of practice. It’s sometimes useful to teach these to parents as well so they know how math is being taught. This can help them practice it the “right” way at home.
Use Manipulatives to Help Combine Regrouping and New Math
With either of these techniques, you can help your students by using math manipulatives. I personally like using Base Ten Blocks because you have to count by 10’s. I also have used money because money is in 10’s and 1’s. So, if you’re looking at dimes and pennies, this makes it super simple.
You can combine regrouping with new math to make your math lessons dynamic. Giving your students several different techniques to complete one math problem can really help them thrive in math. Because you’re showing multiple techniques, students are getting to take some ownership in their learning which makes teaching easier for you and learning easier for them.
Here’s a little math freebie for you. Teaching math with playing cards is so much fun and engaging. To get your own copy, fill in the form below.
